SOFIA, March 10 (Reuters) - Bulgarian right-wing activists backed by the opposition GERB party demanded on Monday a referendum to challenge the voting rules in the Balkan country in what has become an increasingly divisive issue in the run up to European vote this May.

About 150 people marched from Sofia University to the parliament building in downtown Sofia and submitted more than 560,000 signatures to parliament calling for the referendum - above the half million they need to force a plebiscite.

Recent opinion polls show the Socialists and centre-right GERB are running neck-to-neck in support ahead of the May election.

An initiative committee collected the signatures for less than a month after the ruling Socialists indicated they would not support the proposal by President Rosen Plevneliev for such a vote.

"The signatures were collected with the energy of the protests of the Bulgarian citizens...not just the GERB party. We want to make the referendum obligatory so that the ruling stop weaselling and appoint it," Sofia University lecturer Georgi Bliznashki told reporters.

The government looked as though it might fall last year when thousands of Bulgarians took to the streets in anti-corruption protests. The protests have since dwindled and analysts say it will limp on at least until the May vote.

The signatures were collected by the GERB party, the rightist Reformist Bloc and protest groups and movements that stood behind anti-government protest last year.

STRENGTHEN TRUST?

In January, Plevneliev, who was elected on GERB's ticket in 2011 and is at odds with the government, proposed that Bulgarians should have their say on whether they want to elect some lawmakers directly rather than from party lists, voting made obligatory and electronic voting allowed.

The parliament of the EU country has approved a new voting code which did not support any of the proposals the president and the right-wing opposition believe would strengthen public trust after last year's massive protests.

A parliamentary commission, where the Socialists have a fragile majority with the silent support of the nationalist Attack party, has already rejected the president's proposal, saying the questions were either unacceptable or vague.

The Socialists have argued compulsory voting may breach the constitution, as voting is a right and not an obligation, and that electronic voting can easily be manipulated.

Parliament will have three months to check the collected signatures and decide whether to allow the referendum to take place. It may still reject it, if it finds the questions raised breach the country's constitution.